Huh. I may be tripping from too much overthought replays, but a lot of Spamton comments towards Kris makes me believe that the soul is Kris's, and is just being puppeted by us, rather than the prevalent theory that it's our soul in him. Kris gets shaken up by Spamton so I am inclined to take what he says with at least some consideration.
I've been leaning towards that outlook as well somewhat. Mainly because it feels like Spamton wouldn't shake him up as much if he was just housing someone else's soul and that was the end of it.
If we say it's Kris's soul and treat that as fact, that does start to raise a lot of interesting questions. Chiefly the question of whether or not Kris knows what happened to his soul one day. I doubt he'd consent to any of this, his treatment of the soul makes it seem like he wants as little to do with it as possible.
That said, whatever Gaster was doing at the start is clearly related to our connection to Kris, though that process was intercepted. Why it was intercepted is another matter entirely.
If Kris isn't aware of us being connected to him, it'd click pretty well with some of the themes we've seen of Kris trying to repress violent tendencies and his desire to be perceived as "normal". Because from his perspective he's just trying to live his life and be normal, repressing this part of himself, and then one day he's been pretty much possessed, with ripping his own soul out being the only way to regain his full agency. At that point he'd probably see us as the manifestation of the very shit he's trying to repress, which yeah, no wonder he doesn't hesitate to treat us the way he does.
As for the process that connected us to Kris, I think it's some form of experiment. He's a scientist that was scattered across time and space, yet somehow survived. He's become aware and is viewing his world from another plane of reality. How I see it, the entire process at the start of Chapter 1 is trying to initiate some way to measure and observe the actions of unknowable and typically unobservable gods. By "unobservable gods" what I mean is that Toby's likes to screw with meta concepts, and to the characters in this world, the players(as in irl people) are a complete anomaly—We don't exist, we can't be reliably observed and we can't be measured, yet somehow we can influence this world and have an impact on it.
Whatever state he's in and goal he's trying to achieve I think he's also well aware that messing around with something that can possess a soul and typically can't be measured or observed is a dangerous game.
Back in Undertale the only people who directly said Gaster's name were the Gaster Followers.
At the start of Chapter 1 in Deltarune, Gaster is deliberately trying to establish a connection with us. If you name the vessel or yourself "Gaster", the game shuts off.
I'd say to him it's the equivalent of getting on CB radio and instantly getting phonebooked by the first person you make contact with. He knows his name is something that shouldn't exist anymore, and we somehow have this unknowable knowledge. He's shutting off the transmitter out of fear.
Apologies for slight Gaster tangent there, your thoughts on Kris being shaken up by the Spamton fight just reminded me of some things I've been mulling over for a while.